Dirty corner behind the corner sofa? What is that?

Was the couch placed against the wall? There will be mildew or mold, I can’t comment on your critters ^^

Yes, the couch was against the wall - now it is about 1cm away. Although with children throwing themselves on it, the gap probably won’t last long.

I would guess booklice.
Just type booklice into Google, then there’s a page from DSV
German Pest Control Association... fits with the dust you have.

https://www.hausbau-forum.de/threads/was-sind-das-für-viecher-und-wo-kommen-sie-her.33905/

The same critters?

Looks just like it: booklice!

And the yellow spots on the wood? Are those eggs? Does the wood react?

Feeding marks and pests as well.
Damp in the corner or just residual moisture in the new building

Residual moisture from the new building is quite possible, we moved in 3 years ago.
What do you mean by feeding marks? The spots on the wall?

Thanks for your answers!

And the yellow dots on the wood? S

Eggs or droppings